USE OF INTERNET TO DO EXPERIMENTS IN DYNAMICS AND CONTROL FROM ZACATECAS MEXICO IN THE LABORATORY OF THE UNIVERSITY OF TENNESSEE AT CHATANOOGAA.

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1 USE OF INTERNET TO DO EXPERIMENTS IN DYNAMICS AND CONTROL FROM ZACATECAS MEXICO IN TE LABORATORY OF TE UNIVERSITY OF TENNESSEE AT CATANOOGAA. Jim enry *, Joé Alberto González Guerrero, Benito Serrano Roale.. The Univerity of Tenneee at Chattanooga, 65 McCallie Ave., Chattanooga, TN Univeridad Autonoma de Zacateca, Unidad Academica de Ciencia Quimica, Camu Siglo XXI, Edificio 6, Carr. a Guadalajara m. 6, Ejido la Econdida, Zacateca Zac., 9860, Mexico, benierra@rodigy.net.mx Phone Ext 637 Abtract The internet wa ued to do remote exeriment in Univeridad Autonoma de Zacateca Mexico, uing the laboratorie in the Univerity of Tenneee at Chattanooga, ecifically, the ytem of two non-interacting tank. In the firt art, te and ule erturbation were alied, and in the econd art, a roortional controller wa ued and te erturbation on the et oint wa alied. The mathematical model were deducted in all the cae, linearizing the exreion for the flow between tank and. In all the cae, the agreement between exerimental and redicted reult wa very good, indicating the model were concetually correct, and the mot imortant, the ue of remote laboratory wa oible and allowed a relationhi between two univeritie. Introduction Currently, the ue of internet to do exeriment in a remote laboratory i a reality. The exeriment were erformed in the Program of Chemical Engineering, Faculty of Chemical Science, Autonomou Univerity of Zacateca Mexico, at any day, any time, uing the two noninteracting tank in the laboratory of the Univerity of Tenneee at Chattanooga. Each tank wa 6 inche in diameter and inche in height. The feed from the firt tank to the econd tank i by gravity (See figure ). A mathematical model wa contructed and it wa neceary to linearize it. Exerimentation The firt erturbation wa to turn on the equiment of the two non-interacting tank and to let it to reach the teady tate, which mean a te erturbation. The imlementation of an interface through internet htt://flow.engr.utc.edu:443/ allow acce to thi iece of equiment from anywhere in the world. See figure. The firt art of the exerimental ection wa to run ome exeriment for different value of the um. In the econd art, one te erturbation wa alied, with magnitude A, and in other exeriment, after the tart of the equiment, a ule erturbation wa alied. For both cae, the

2 reone of the height of the level of the econd tank wa regitered, and the exerimental reult were comared with the rediction of the model. In the third art, the exeriment were erformed with te erturbation, regulated by a roortional controller. Figure.- Sytem of two non-interacting tank. Figure.- Screen to elect the iece of equiment. Click the link Tank Water Level Control Contant Inut or Ste Inut.

3 Figure 3.- Screen to tart the exeriment with the ytem of two non interacting tank. A tyical exeriment for the tart of the exeriment i hown in figure 3, with 00% of the caacity of the um. It i oberved that the teady tate height of the level in tank,.5, i reached in 50 econd. Figure 4.- Level of tank, with 00 % caacity of the um.

4 The next exeriment wa to work with the um at it 80 % of caacity, and to aly a te erturbation of 0 %. Figure 5 how the reult of thi exeriment. Figure 5.- Reone of the level of tank to a te erturbation. The next exeriment wa carried out with the caacity of the um of 70 %. Once the tady tate wa reached, a ule erturbation wa alied increaing the um caacity in other 30%, for 00 econd. After thi eriod, the um wa returned to 70 %. The reult are hown in figure 6. Figure 6.- Reone of the level of tank under a ule erturbation of 00 econd.

5 In the next exeriment, the um wa oerated at 60 % of it caacity, uing a roortional controller with gain 0. After the teady tate wa reached, a te erturbation wa alied increaing another 40 %. Several value of the gain were ued. The exerimental reult are hown in Figure 7. It i oberved that increaing the value of the gain, an untability i generated, a it i redicted by theory. Figure 7.- Reone of the level of tank under a te erturbation for everal value of the gain of the roortional controller. It i very imortant to note that all thee exeriment were done uing internet, in the laboratory of Unvierity of Tenneee from the Autonomou Univerity of Zacateca, Mexico. Mathematical modeling. The ma balance for tank and are: q q i ( t) q ( t) ( t) q ( t) A T dh dt ( t) ( t) dh AT, dt Uing the Taylor erie, the linearized exreion for q(t), the flow leaving tank i obtained:

6 q ( t) q ( h ( ) h ) R The tranfer function for thi ytem of non interacting tank for the liquid level of the econd tank i: ( ) τ A T Q i ( ) τ τ Where: D D 6in 5. 4, h 7., 30 3 A T AT τ R A T.637, R A T 3.99, R h 0. 7 Cv τ R Cv C C [ ( t) ] g vt v ρr g v c h 5 Cv i the econdary coefficient of valve in tank. Cv i the econdary coefficient of valve in tank.

7 CvT coefficient of valve in tank CvT coefficient of valve in tank Pv (t) oition of the valve oening in tank. Pv (t) oition of the valve oening in tank. If we aly a te erturbation, with magnitude, and with tranfer function /. The reone of the econd tank i: Subtituting the ecific value, we obtain: The comarion of the rediction of thi equation with the exerimental reult obtained after uing the remote laboratory of the Univerity of Tenneee camu Chattanooga, are hown in Figure. In thi cae, the agreement i very good. Figure 8.- Comarion between the mathematical model and exerimental reult for a te erturbation. Now, alying a rectangular ule of magnitude and duration T, The reone i:

8 ,, The numerical value are: 3 h, 45, T 00, R , C v Subtituting thee value in the ule reone: 5 A comarion between the exermiental and calculated reult i hown in figure. The agreement during the firt tage are excellent, however, ome diference i oberved after the erturbation. Figure 9.- Comarion between the mathematical model and exerimental reult for a ule erturbation.

9 Exeriment were alo erformed uing a roortional controller. The block diagram i hown in the following figure: Where: R() Set oint. Q i () Flow entering the firt tank, or load variable. C() Controller tranfer function. P() Tranfer function for the roce of two non-interacting tank. M() Tranfer function of the meaurement device. () Tranfer function of the level of the econd tank, or exit variable. The following tranfer function i obtained: C ( ), P( ), M ( ) Performing algebra: τ A T τ τ

10 ( ) τ A T τ A T Performing the invere tranform: ( t) ( )( ) τ A ( )( ) T t t τat τat ( ) τat ( ) e Where: 30, τ AT , x0 e x0, 9.54x x x x x x0 ( ) x x0 ( ) x x0 The comarion between the exerimental and redicted reult i done in figure 0. Figure 0.- Comarion of exerimental and redicted reult uing a te erturbation and a roortional controller.

11 Certainly, the agreement i not very good but the model indicat very well the tendency of the exerimental reult. Concluion..- The agreement between the exerimental and modelled reult i good, and thi validate the mathematical model, which i able to redict the reone of the ytem to any te erturbation, whether at the tart or after a teady tate i reached..- In general, the model uing a ule erturbation i concetually correct and reroduce the exerimental data, in ite of after the erturbation, ome diference between data i oberved. 3.- The mathematical model uing roortional controller redict the reone tendency when the value of c i increaed, indicating that the model i concetually correct. Reference..- Donald R. Coughanowr, Proce ytem analyi and control, Mc. Graw ill, econd edition, Wodek. Gawronki, Advanced Structural Dynamic and Active Control of Structure, Sronger, 004.